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Development of software to aid researches in Kleinnian groups and hyperbolic geometry

Research Project

Project/Area Number 14540079
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionNara Women's University

Principal Investigator

WADA Masaaki  Nara Women's University, Info. & Comp.Sci., Prof., 理学部, 教授 (80192821)

Co-Investigator(Kenkyū-buntansha) YAMASHITA Yasushi  Nara Women's Univ., Info. & Comp.Sci., Assoc.Prof., 理学部, 助教授 (70239987)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2004: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2003: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
KeywordsKleinnian Groups / Hyperbolic Geometry / Research Aid / Software
Research Abstract

The head investigator is developing and distributing publicly the program OPTi. The program has been used by many researchers in Kleinnian groups and hyperbolic geometry, including such famous names as Troels Jorgensen (Columbia Univ.), Albert Marden (Univ.Minnesota), and William Thurston (UC Davis). The goal of this research project was to further refine OPTi to make it a more useful tool for researchers in Kleinnian groups and hyperbolic geometry. At the same time, we also wanted to make OPTi an effective educational device by improving its user interface and making OPTi easy to use for both researchers and students.
After four years of continued improvements and diligent popularization of the program, we think the goal has been achieved. OPTi's web site (http://vivaldi.ics.nara-wu.ac.jp/~wada/OPTi/) is accessed from all over the world, as can be seen from the fact that the web site is ranked highly in the Topology Software category of Google's directory. Nowadays, OPTi is one of the most important research tools and educational aids for Topologists of the world.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (19 results)

All 2005 2003 2000 Other

All Journal Article (15 results) Publications (4 results)

  • [Journal Article] Twisted Alexander polynomials and subjectivity of a group homomorphism2005

    • Author(s)
      T.Kitano 他
    • Journal Title

      Algebraic & Geometric Topology 5

      Pages: 1315-1324

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Twisted Alexander polynomials and surjectivity of a group homomorphism2005

    • Author(s)
      T.Kitano, et al.
    • Journal Title

      Algebraic & Geometric Topology Vol.5

      Pages: 1315-1324

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Twisted Alexander polynomials and surjectivity of a group homomorphism2005

    • Author(s)
      T.Kitano, M.Suzuki, M.Wada
    • Journal Title

      Algebraic & Geometric Topology 5

      Pages: 1315-1324

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Jorgensen's picture of punctured torus groups and its refinement2003

    • Author(s)
      H.Akiyoshi 他
    • Journal Title

      Lond. Math. Soc. Lec. Notes 299

      Pages: 247-273

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] OPTi's Algorithm for Drawing the Limit Set2003

    • Author(s)
      M.Wada
    • Journal Title

      Interdisciplinary Information Sciences 9

      Pages: 183-187

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Jorgensen's picture of punctured torus groups and its refinement2003

    • Author(s)
      H.Akiyoshi, et al.
    • Journal Title

      Kleinian Groups and Hyperbolic 3-Manifolds, Lond.Math.Soc.Lec.Notes (Cambridge Univ.Press) 299

      Pages: 247-273

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] OPTi's Algorithm for Drawing the Limit Set2003

    • Author(s)
      M.Wada
    • Journal Title

      Interdisciplinary Information Sciences Vol.9

      Pages: 183-187

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A way from punctured torus groups to two-bridge knot groups2000

    • Author(s)
      H.Akiyoshi 他
    • Journal Title

      Geometry and Topology, Proceeding of Workshop in Pure Mathematics 19

      Pages: 145-173

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A way from punctured torus groups to two-bridge knot groups2000

    • Author(s)
      H.Akiyoshi, et al.
    • Journal Title

      Geometry and Topology, Proceeding of Workshop in Pure Mathematics (Pure Mathematics Research Association, The Korean Academic Council) Vol.19

      Pages: 145-173

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Drawing Bers Embeddings of the Teichmuller Space of Once-punctured Tori

    • Author(s)
      Y.Komori 他
    • Journal Title

      Experimental Mathematics 印刷中

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] OPTi's Algorithm for Discreteness Determination

    • Author(s)
      M.Wada
    • Journal Title

      Experimental Mathematics 印刷中

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Drawing Bers Embeddings of the Teichmuller Space of Once-Punctured Tori

    • Author(s)
      Y.Komori, et al.
    • Journal Title

      Experimental Mathematics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] OPTi's Algorithm for Discreteness Determination

    • Author(s)
      M.Wada
    • Journal Title

      Experimental Mathematics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] OPTi's Algorithm for Discreteness Determination

    • Author(s)
      M.Wada
    • Journal Title

      Experimental Mathematics (to appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Drawing Bers Embeddings of the Teichmuller Space of Once-Punctured Tori

    • Author(s)
      Y.Komori, T.Sugawa, M.Wada, Y.Yamashita
    • Journal Title

      Experimental Mathematics (to appear)

    • NAID

      110000164658

    • Related Report
      2005 Annual Research Report
  • [Publications] Masaaki Wada: "OPTi's algorithm for drawing the limit set"Interdisciplinary Information Sciences. 9. 183-187 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Akiyoshi, M.Sakuma, M.Wada, Y.Yamashita: "Jorgensen's picture of punctured torus groups and its refinement"Kleinian Groups and Hyperbolic 3-Manifolds, Lond.Math.Soc.Lec.Notes. 299. 247-273 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Masaaki Wada: "OPTi's algorithm for drawing the limit set"Interdisciplinary Information Sciences. 9. (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Akiyoshi, M.Sakuma, M.Wada, Y.Yamashita: "Jorgensen's picture of punctured torus groups and its refinement"Kleinian Groups and Hyperbolic 3-Manifolds, Lond. Math. Soc. Lec. Notes. 299. (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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